📋 Session plan (for teachers)

Session 3 — Division: sharing and grouping

Grade 3 · Math for Young Minds Total time: ~22 minutes Common Core: 3.OA.A.2, 3.OA.B.6 Today's idea: Division splits a total into equal shares — and it's the opposite move from multiplication.

What students will be able to do

By the end of this session, the student can:

• See division as the opposite move from multiplication.
• Use sharing: split a total equally among a known number of groups.
• Use grouping: split a total into groups of a known size.
• Connect a division sentence like 12 ÷ 4 = 3 to a multiplication fact like 4 × 3 = 12.

Materials

• ~20 small counters per pair (paper cookies, beans, or cubes)
• 4–5 small paper plates or napkins per pair
• Worksheet (one per student)
• Pencils

Substitution: No plates? Draw 4–5 circles on a sheet of paper. Any small objects work for counters — buttons, coins, scraps of paper.

New words

Heads-up — common confusions

• Order matters in division. 12 ÷ 4 is not the same as 4 ÷ 12. This is different from multiplication — worth naming out loud.
• Sharing and grouping are both division. They ask slightly different questions, and both are okay.
• Some kids will end up with leftovers and not name them. Today's totals all divide evenly — no remainders yet.
• The ÷ sign is new. Say "divided by" out loud the first few times.

Plan

1 · Hello & today's idea — 2 min

"Last time we made equal groups with multiplication. Today we go the other way. We start with a total and split it into equal shares."

Hold up 12 counters (paper cookies).

Ask: "If I have 12 cookies and 4 friends, how do I make it fair?"

Take a few quick answers. Don't solve it yet — that's the next block.

2 · Hands-on explore — 7 min

Hand each pair:

• 12 counters
• 4 plates

Prompt: "You have 12 cookies and 4 friends. Put the cookies on the plates so every friend gets an equal share. How many does each friend get?"

Let them work. Listen for:

• Are they dealing one-by-one, like cards?
• Are they trying to guess and check?
• Do they notice when the plates are uneven?

After ~3 minutes, pause:

"How many cookies on each plate? How did you know it was fair?"

Take 2–3 responses. You're listening for "3 on each plate" and "every plate has the same".

Now switch the question:

"New problem. Take 20 counters. Put them in piles of 5. How many piles do you make?"

Let them try it. This is the same idea — division — but asking a different question.

3 · Connect to the math — 4 min

Name what just happened.

"Splitting a total into equal shares is called division. The sign we use is ÷ — we say 'divided by'."

Write on the board:

   12   ÷   4   =   3
    ↑        ↑       ↑
 cookies  friends  each
  total            friend
                    gets

Read it out loud: "12 divided by 4 equals 3."

Then write underneath:

   4   ×   3   =   12

"See that? Division and multiplication are two sides of the same coin. If 12 ÷ 4 = 3, then 4 × 3 = 12."

Quick note:

"Today we asked two kinds of questions. Sharing — 'how many for each friend?' Grouping — 'how many piles of 5?' Both are division."

4 · Practice with support — 7 min

Pass out the worksheet.

Do problem 1 together out loud, using counters and plates on the board:

"Share 12 cookies among 4 friends. How many does each friend get?" → 3. Write 12 ÷ 4 = 3.

Then students try problems 2 and 3 on their own or with a partner:

• Problem 2 (solo): Share 15 stickers among 3 kids. How many for each kid? → 5
• Problem 3 (solo): Put 20 pencils into groups of 5. How many groups? → 4

Circulate. If a student is stuck, hand them counters and say "act it out first."

Problem 4 (stretch): "You know 12 ÷ 4 = 3. Without computing, what is 4 × 3? And 3 × 4?" → 12 for both.

5 · What we did + Try at home — 2 min

"Today you learned that division splits a total into equal shares. The sign ÷ means 'divided by'. And every division sentence has a multiplication partner."

Hand out the take-home:

"Find a small pile of something at home — snacks, toys, coins. Share it equally with someone in your family. Count how many each person gets. Write the division sentence."

Observation rubric — what to notice in this session

Use this during the session, not as a test. One observation per student is plenty.

No fail state. "Developing" today is "using" next week.

What's next (Session 4)

Building on this, Session 4 — Multi-step word problems puts × and ÷ together. Now that you know both moves, we tackle word problems that take more than one step.

✏️ Worksheet (for students)

Math for Young Minds · Grade 3

Session 3 — Division: sharing and grouping

[ Hello ]  →  [ Explore ]  →  [ Connect ]  →  [ Practice ← we are here ]  →  [ Try at home ]

Today's big idea

Division means splitting a total into equal groups.

The sign ÷ is read as "divided by".

So 12 ÷ 4 means "12 split into 4 equal groups".

Example we did together

   12 cookies                4 friends

   🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪      🙂  🙂  🙂  🙂

   Share them out, one by one...

   🙂        🙂        🙂        🙂
   🍪🍪🍪    🍪🍪🍪    🍪🍪🍪    🍪🍪🍪

         12   ÷   4   =   3

We say it: "12 divided by 4 equals 3." Each friend gets an equal share of 3 cookies.

Problem 1 — together

Share 12 cookies among 4 friends. How many cookies does each friend get?

Draw 4 plates. Place the cookies one at a time until they are gone.

┌─────────────────────────────────────────────────────────┐
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Write the division sentence:

  ____  ÷  ____  =  ____
  total    friends   each

Problem 2 — on your own

Share 15 stickers among 3 kids. How many stickers does each kid get?

Draw 3 kids and share out the stickers:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Write the division sentence:

  ____  ÷  ____  =  ____

Problem 3 — on your own

Put 20 pencils into groups of 5. How many groups can you make?

This one is different! You know the size of each group (5). Find how many groups fit.

Draw 20 pencils, then circle groups of 5:

┌─────────────────────────────────────────────────────────┐
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
│                                                         │
└─────────────────────────────────────────────────────────┘

Write the division sentence:

  ____  ÷  ____  =  ____

Problem 4 — stretch

You already know:

   12   ÷   4   =   3

Without computing, fill these in:

• 4 × 3 = ____
• 3 × 4 = ____

Hint: division and multiplication are two sides of the same coin. If you know one, you know the others!

Now try this one. If 15 ÷ 3 = 5, then:

• 3 × 5 = ____

Today's words

Try at home tonight (1 minute)

Find a small pile of something at home. Share it equally with someone in your family. Count how many each person gets, then write the division sentence.

Examples:

• 🍇 Grapes shared between two siblings
• 🧸 Toys split among stuffed animals
• 🪙 Coins divided into stacks of 5
• 🍪 Crackers shared at snack time
• 📚 Books arranged into equal piles on the shelf

  ____  ÷  ____  =  ____
  total   groups   each

Show a grown-up tomorrow morning.

Next time: we put × and ÷ together to solve bigger word problems!

🏠 Family guide (for parents)

Math for Young Minds · Grade 3 · Session 3

A note for grown-ups: today we started division

What your child did today

In class today, we explored division for the first time.

The big idea: division is the opposite move from multiplication. It splits a total into equal groups.

We started with cookies. Twelve cookies, four friends → each friend gets 3 cookies. Then we tried it a different way: 20 pencils put into groups of 5 → that makes 4 groups.

Both moves are division. One asks "how many in each group?" The other asks "how many groups?" Your child saw that 12 ÷ 4 = 3 is the same family as 4 × 3 = 12.

Why this matters

Division can feel tricky because it's multiplication run backwards. We took it slow today with real objects on plates — that's how the idea sticks.

We're not memorizing division facts yet. We're noticing that splitting into equal groups is a real, everyday move. No timed tests. Understanding first. Speed comes later, on its own.

🏠 Try this tonight (1 minute)

Find a small pile of something at home. Share it equally with someone in the family. Count how many each person gets. Then write the division sentence together — like 10 ÷ 2 = 5.

Easy starters around the house:

A short script, if it helps:

• "How many do we have in total?"
• "How many people (or groups) are we sharing with?"
• "How many does each one get?"

Pick numbers that come out even tonight. Leftovers are a great topic — just not today.

Words your child is learning

• Division — splitting a total into equal groups
• ÷ — the sign we read out loud as "divided by"
• Equal share — the same amount for each group or person

If your child says…

"This is easy." Great. Ask them to flip it: if 12 ÷ 4 = 3, what's 4 × 3? Then ask them to make up their own sharing problem for you.

"This is hard." Also great. Get real objects on the table — beans, coins, cereal. Make the plates or piles by hand. Count what ends up in each one. The symbol can wait.

"I don't want to." That's okay. Try once with something they care about — their snack, their toys. Keep it under a minute. If it's still a no tonight, try again tomorrow. We're not in a rush.

A small heads-up

Unlike multiplication, order matters in division. 12 ÷ 4 is not the same as 4 ÷ 12. If your child mixes them up, that's normal — it's a new idea. Gently restate which number is the total and which is the groups.

What's next

In our next session, your child will start multi-step word problems. Now that they know × and ÷, we put them together in problems that take more than one step.

Thanks for taking a minute tonight. These small kitchen-table moments are where math lives.

— Math for Young Minds

🔑 Cheat sheet (visual)

🔑 Division = splitting into equal groups

Picture 1 — Sharing cookies 🍪

   12 cookies  →  shared among 4 friends

   👦         👧         🧒         👶
   🍪🍪🍪    🍪🍪🍪    🍪🍪🍪    🍪🍪🍪

       12  ÷  4  =  3   (each friend gets 3)

Each friend gets an equal share. ✨

Picture 2 — Grouping pencils ✏️

   20 pencils  →  put into groups of 5

   ✏️✏️✏️✏️✏️   ✏️✏️✏️✏️✏️   ✏️✏️✏️✏️✏️   ✏️✏️✏️✏️✏️
    group 1       group 2       group 3       group 4

       20  ÷  5  =  4   (we made 4 groups)

How to read the sign ÷

                ┌──── how many groups   (or size of each group)
                │
       12  ÷   4   =   3
       │               │
       │               └── how many in each group  (or # of groups)
       └──── total to split

Say it out loud: "12 divided by 4 equals 3."

Two questions, both are division

⚠️ Order matters!

      12 ÷ 4  =  3        ✅
       4 ÷ 12 =  ???      ❌  not the same!

(Different from ×, where 3 × 4 = 4 × 3.)

Division ↔ Multiplication (two sides of the same coin) 🪙

       ● ● ●               If you know:
       ● ● ●                  12 ÷ 4 = 3
       ● ● ●
       ● ● ●               Then you know:
                              4 × 3 = 12
   4 rows of 3 = 12           3 × 4 = 12

Try this in your head

   🍇🍇🍇🍇🍇🍇🍇🍇🍇🍇🍇🍇🍇🍇🍇

   15 grapes shared among 3 kids

➤ ____ ÷ ____ = ____ each

Answer: 15 ÷ 3 = 5